Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
long i, n, pr[45050];
bool flag;
void search(long low, long high, long p) {
  if (high < low || flag == 0) return;
  long mid = (high + low) / 2;
  if (pr[mid] == p) {
    flag = 0;
    return;
  } else if (pr[mid] > p)
    search(low, mid - 1, p);
  else
    search(mid + 1, high, p);
}
int main() {
  for (i = 1; i < 45000; i++) pr[i] = (i * (i + 1)) / 2;
  while (~scanf("%ld", &n)) {
    flag = 1;
    for (i = 1; i < 45000; i++) {
      search(1, 45000, n - pr[i]);
      if (flag == 0) break;
    }
    if (flag)
      printf("NO\n");
    else
      printf("YES\n");
  }
  return 0;
}